Question

2) A steel rod with a cross-sectional area of 0.25 sq. in. is stretched between two fixed points. The tensile load at 70 degrees F is 1200 lb. What will be the stress at 0 degrees F? At what temperature will the stress be zero?

Assume ? = 6.5 x 10^-6 °F^-1 and E = 30 x 10⁶ psi.

Answer 1

Initial stress in rod = tensile load / area = 4800 psi
With decrease in tempreture, natural length of rod decrease. As rod is under tension and end points are fixed, there is increase in tension or stress in the rod.
Increase in stress = E ( delta L / L)
                             = E ( )
                             = 30x10⁶ *6.5x10^-6*70
                              = 13650 psi
Stress at 0 deg F = 13650 + 4800 = 18450 psi

To make stress equal to zero, we have to decrease tension. So tempreture of rod must be increased.
Change in stress = 4800 = E ( )
                            4800 = 30x10⁶ *6.5x10^-6
                             = 24.6 deg F
Tempreture of rod for stress to be zero = 70 + 24.6 = 94.6 deg F